Structurally, few swords could withstand parrying with the side of the blade. But there is a lot of territory between the choices of edge or side.
Few swords could withstand a 90 degree block on any side, which is why one is trained specifically not to do that. Only shields and the heaviest of armor could realistically stand up to something like that, and even then, it isn't advisable. It is always better to block at an angle than straight on, because this deflects the energy rather than tries to stop it entirely. A good example is this image:
And, if the observer notices, he is blocking with the side of the katana. It looks like his next move is to slide his left leg back, regrip the katana with two hands, and perform a vertical cut to the opponent's neck. Regardless, his intention is to cause the downward cut from the opponent to slide off and away from himself.
Now, the point I was trying to make above is that there isn't a single "Swordsmen everywhere will do..." because what they do will depend on how well they were trained (or not trained), in what style they were trained, what weapon(s) they are using, and what era they are fighting in. Again, in the broadest of terms, if the sword is sharpened to the crossguard, the blade edge is not intended for defense, and defense is either with the side edge or another weapon (shield, parrying blade, etc.). If part of the blade is dulled or still rectangular (like a claymore), that portion may be used for defense. But, again, that is in broad terms, so there are exceptions, I am sure, and it doesn't take into account novices.
(I should also note that I am using block, parry, and defense more or less interchangeably, but this is for ease of communication rather than technical accuracy. A parry is technically a redirection, while a block is a stopping of the attack, and defense is the blanket term for both. True blocks are rather rare in armed combat, because of the risk involved. Parries are far more common.)